Solve 1/4*314*48^2x

$$\frac { 1 } { 4 } \times 314 \times 48 ^ { 2 } x$$

Evaluate

$$180864x$$

Solution Steps

Multiply \frac{1}{4} and 314 to get \frac{314}{4}.

$$\frac{314}{4}\times 48^{2}x$$

Reduce the fraction \frac{314}{4} to lowest terms by extracting and canceling out 2.

$$\frac{157}{2}\times 48^{2}x$$

Calculate 48 to the power of 2 and get 2304.

$$\frac{157}{2}\times 2304x$$

Express \frac{157}{2}\times 2304 as a single fraction.

$$\frac{157\times 2304}{2}x$$

Multiply 157 and 2304 to get 361728.

$$\frac{361728}{2}x$$

Divide 361728 by 2 to get 180864.

$$180864x$$

Differentiate w.r.t. x

$$180864$$

Steps Using Definition of a Derivative

Multiply \frac{1}{4} and 314 to get \frac{314}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{314}{4}\times 48^{2}x)$$

Reduce the fraction \frac{314}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{157}{2}\times 48^{2}x)$$

Calculate 48 to the power of 2 and get 2304.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{157}{2}\times 2304x)$$

Express \frac{157}{2}\times 2304 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{157\times 2304}{2}x)$$

Multiply 157 and 2304 to get 361728.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{361728}{2}x)$$

Divide 361728 by 2 to get 180864.

$$\frac{\mathrm{d}}{\mathrm{d}x}(180864x)$$

The derivative of ax^{n} is nax^{n-1}.

$$180864x^{1-1}$$

Subtract 1 from 1.

$$180864x^{0}$$

For any term t except 0, t^{0}=1.

$$180864\times 1$$

For any term t, t\times 1=t and 1t=t.

$$180864$$